Can you help me win the lottery?

21st February, 2009

Dear Economist,

I have started playing the national lottery in an attempt to resolve my worsening financial situation. While I am aware of the improbability of winning, I was wondering if I would improve my chances by sticking with the same numbers rather than using the randomly generated “quick pick”?
Peter, Canada

Dear Peter,

You seem to have a rather charming scenario in mind, with you playing the role of a little lost child, and the lottery machine playing the role of parent, diligently searching for you. This is called a “rendezvous problem”, and, in general, you would be better off staying where you are and letting the lottery machine find you.

With almost 14 million combinations to try, this would take, on average, seven million attempts – about 67,000 years if you play twice a week. Success would be guaranteed after 135,000 years. If you choose your numbers at random, however, success is never guaranteed, and tame mathematicians tell me that the average time to strike lucky is also longer – perhaps 100,000 years or so.

But whether you can shave 35,000 years off is beside the point. The lottery machine is not trying to find your number. It has no memory of previous combinations, and is equally (un)likely to pick any of the 14 million. Pick at random, write down your birthday … it makes no difference to your chance of winning – although if you write down unusual numbers, it will minimise the likelihood that if you win, you’ll have to share your prize.

In case you are not a long-time reader, I will repeat my advice as to how to enjoy the thrill of the lottery without the fool’s bet. Choose your numbers, but don’t buy a ticket. You’ll win almost every week – the fear that your number might actually come up is an adrenaline rush to beat them all.

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